What is the general solution for csc^2(x)=-2cot(x) ?

The general solution for csc^2(x)=-2cot(x) is x=(3pi)/4+pin

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csc^2(x)=-2cot(x)

csc^{2} (x) = - 2 cot (x)

x = \frac{3 π}{4} + πn

Solution steps

csc^{2} (x) = - 2 cot (x)

Subtract

- 2 cot (x)

from both sides

csc^{2} (x) + 2 cot (x) = 0

Rewrite using trig identities

1 + cot^{2} (x) + 2 cot (x) = 0

Solve by substitution

cot (x) = - 1

cot (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn

tan^{2} (θ) + cot^{2} (θ) = - 1

sin^{2} (θ) + cos (2 θ) - cos (θ) = 0

4 cos^{2} (x - 3) = 0

2 sin^{2} (A) + sin (A) = 0

3 sin^{2} (x) - 2 sin (x) - 5 = 0

What is the general solution for csc^2(x)=-2cot(x) ?
The general solution for csc^2(x)=-2cot(x) is x=(3pi)/4+pin